Problem: Simplify the following expression: $z = \dfrac{3a^2 + 3a - 36}{a + 4} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $3$ , so we can rewrite the expression: $ z =\dfrac{3(a^2 + 1a - 12)}{a + 4} $ Then we factor the remaining polynomial: $a^2 + {1}a {-12} $ ${4} {-3} = {1}$ ${4} \times {-3} = {-12}$ $ (a + {4}) (a {-3}) $ This gives us a factored expression: $\dfrac{3(a + {4}) (a {-3})}{a + 4}$ We can divide the numerator and denominator by $(a - 4)$ on condition that $a \neq -4$ Therefore $z = 3(a - 3); a \neq -4$